Browse > Article
http://dx.doi.org/10.14403/jcms.2011.24.2.21

NEW EXACT TRAVELLING WAVE SOLUTIONS FOR SOME NONLINEAR EVOLUTION EQUATIONS  

Lee, Youho (Department of Internet Information, Daegu Hanny University)
An, Jaeyoung (Department of Mathematics, Sungkyunkyawn University)
Lee, Mihye (Department of Mathematics, Sungkyunkyawn University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.2, 2011 , pp. 359-370 More about this Journal
Abstract
In this work, we obtain new solitary wave solutions for some nonlinear partial differential equations. The Jacobi elliptic function rational expansion method is used to establish new solitary wave solutions for the combined KdV-mKdV and Klein-Gordon equations. The results reveal that Jacobi elliptic function rational expansion method is very effective and powerful tool for solving nonlinear evolution equations arising in mathematical physics.
Keywords
Klein-Gordon equation; travelling wave solutions; Jacobi elliptic function rational expansion method;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A. Bekir, A. Boz, Exact solutions for nonlinear evolution equations using Exp- function method, Phys. Lett. A 372 (2008), 1619-25.   DOI   ScienceOn
2 A. Bekir, New solitons and periodic wave solutions for some nonlinear physical models by using the sine-cosine method Phys. Scr. 77 (2008) 045008.   DOI   ScienceOn
3 Drazin PG, Johnson RS. Solitons: An Introduction. Cambridge: Cambridge University Press, 1983.
4 El-Wakil SA, Abdou MA. New exact travelling wave solutions using modified extended tanh-function method, Chaos Solitons Fract 31 (2007), 840-52.   DOI   ScienceOn
5 Fan EG, Zhang J. Applications of the Jacobi elliptic function method to special- type nonlinear equations, Phys. Lett. A 305 (2002), 383-92.   DOI   ScienceOn
6 He JH. Variational iteration method: Some recent results and new interpreta- tions, J. Comput. Appl. Math. 207 (2007), 3-17.   DOI   ScienceOn
7 Wazwaz AM. The extended tanh method for the Zakharov-Kuznetsov (ZK) equa- tion, the modified ZK equation, and its generalized forms, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 1039-47.   DOI   ScienceOn
8 Mohamad MNB. Exact solutions to the combined KdV and mKdV equation, Math Meth Appl Sci 1992;15;73   DOI
9 Wu XH, He JH. Solitary solutions, periodic solutions and compacton-like solu- tions using the Exp-function method, Comput. Math. Appl. 54 (2007), 966-86.   DOI   ScienceOn
10 Q. Wang, Y. Chen, HQ. Zhang, A new Jacobi elliptic function rational ex- pansion method and its application to (1+1)-dimensional dispersive long wave equation Chaos Solitons Fract 23 (2005), 477-83.   DOI   ScienceOn
11 S. Zhang, W.Wang, JL. Tong, The improved sub-ODE method for a generalized KdV-mKdV equation with nonlinear terms of any order, Phys. Lett. A 372 (2008), 3808-813.   DOI   ScienceOn